# Curve and surface construction based on the generalized toric-Bernstein basis functions

@article{Li2019CurveAS, title={Curve and surface construction based on the generalized toric-Bernstein basis functions}, author={Jinggai Li and Chungang Zhu}, journal={Open Mathematics}, year={2019}, volume={18}, pages={36 - 56} }

Abstract The construction of parametric curve and surface plays an important role in computer aided geometric design (CAGD), computer aided design (CAD), and geometric modeling. In this paper, we define a new kind of blending functions associated with a real points set, called generalized toric-Bernstein (GT-Bernstein) basis functions. Then, the generalized toric-Bézier (GT-Bézier) curves and surfaces are constructed based on the GT-Bernstein basis functions, which are the projections of the… Expand

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The local controlled generalized H-Bezier model is one of the most useful tools for shape designs and geometric representations in computer-aided geometric design (CAGD), which is owed to its good… Expand

Total Positivity of A Kind of Generalized Toric-Bernstein Basis

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The normalized total positivity of a kind of generalized toric-Bernstein basis is proved and the progressive iterative approximation property of the generalized Toric-Bezier curve is obtained. Expand

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